Global regime for general additive functionals of conditioned Bienaymé-Galton-Watson trees
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DOI: 10.1007/s00440-021-01095-9
Abstract: We give an invariance principle for very general additive functionals of conditioned Bienayme-Galton-Watson trees in the global regime when the offspring distribution lies in the domain of attraction of a stable distribution, the limit being… read more here.
Keywords: global regime; watson trees; galton watson; general additive ... See more keywords
On the transience and recurrence of Lamperti's random walk on Galton-Watson trees
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DOI: 10.1007/s11425-017-9302-9
Abstract: AbstractIn a Galton-Watson tree generated by a supercritical branching process with offspring N and EN:= m > 1, the conductance assigned to the edge between the vertex x and its parent x* is denoted by… read more here.
Keywords: random walk; galton watson; lamperti random;
Random self-similar trees and a hierarchical branching process
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DOI: 10.1016/j.spa.2018.07.015
Abstract: We study self-similarity in random binary rooted trees. In a well-understood case of Galton-Watson trees, a distribution on a space of trees is said to be self-similar if it is invariant with respect to the… read more here.
Keywords: self similar; process; branching process; self similarity ... See more keywords
On the genealogy and coalescence times of Bienaymé–Galton–Watson branching processes
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DOI: 10.1080/15326349.2017.1375958
Abstract: ABSTRACT Coalescence processes have received a lot of attention in the context of conditional branching processes with fixed population size and non-overlapping generations. Here, we focus on similar problems in the context of the standard… read more here.
Keywords: bienaym galton; galton watson; watson branching; genealogy ... See more keywords
Invasion percolation on Galton-Watson trees
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DOI: 10.1214/19-ejp281
Abstract: We consider invasion percolation on Galton-Watson trees. On almost every Galton-Watson tree, the invasion cluster almost surely contains only one infinite path. This means that for almost every Galton-Watson tree, invasion percolation induces a probability… read more here.
Keywords: invasion percolation; galton watson;
Gromov–Hausdorff–Prokhorov convergence of vertex cut-trees of $n$-leaf Galton–Watson trees
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DOI: 10.3150/18-bej1055
Abstract: In this paper we study the vertex cut-trees of Galton-Watson trees conditioned to have $n$ leaves. This notion is a slight variation of Dieuleveut's vertex cut-tree of Galton-Watson trees conditioned to have $n$ vertices. Our… read more here.
Keywords: gromov hausdorff; watson trees; galton watson; prokhorov ... See more keywords
Invariance and attraction properties of Galton–Watson trees
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DOI: 10.3150/20-bej1292
Abstract: We give a complete description of invariants and attractors of the critical and subcritical Galton-Watson tree measures under the operation of Horton pruning (cutting tree laves with subsequent series reduction). The class of invariant measures… read more here.
Keywords: watson trees; watson; galton watson; invariance attraction ... See more keywords